00:01
The very first thing we're going to find here is f of g of x.
00:04
So when we find f of g, that means g is going to be placed into f.
00:08
So what this would be is 2 over and then 1 over x minus 3.
00:14
So what we have to consider here for domain is the g of x means that x cannot be equal to 0.
00:21
So i'm just going to put it out for the side before i simplify.
00:24
So the next thing i'm going to do is multiply top and bottom by x because what that will do is get rid of that fraction.
00:29
So this will simplify down into 2x in the numerator and then 1 minus 3x in the denominator.
00:35
So then this will allow us to see what restrict other restrictions we have on the domain.
00:39
So this would be f of g of x here and then the domain would be can't be equal to zero.
00:45
And then from this denominator here, it looks like we can't also be one third.
00:50
So that would be the very first one.
00:53
The second one is g of f.
00:55
So that's going to have us kind of do the reverse of it.
00:58
So i'm going to take this and put it in it.
00:59
Into 1 over x.
01:01
So it's 1 over 2 over x minus 3.
01:05
So what will happen here is we'll flip and multiply.
01:08
So it'll be 1 times and then x minus 3 over 2, which just simplifies just to that x minus 3 over 2.
01:16
So the restrictions on this is from the original function f of x, we know that x cannot be equal to 3.
01:22
So if you need to do interval notation, you would do negative finity up to 3 and then union with 3 to infinity...